Numerical Methods for Elliptic and Parabolic Partial Differential Equations

There will be no lecture or tutorial in the week of October 18, 2010.

The first lecture is on Tuesday, September 21, 2010 and the tutorials begin on Monday, October 4.

Lecturer: Siddhartha Mishra

Coordinator: Claude Gittelson

Lecture

• Tue 15:15-17:00 HG E 21
  
• Thu 13:15-15:00 HG E 21
  

Tutorial

• Mon 16:15-17:00 ML H 34.3
  

Assignments

Questions? Email the lecturer or coordinator in case of questions concerning the exercises or the lecture, or stop by HG G 56.1 during office hours on Fridays at 12:00 noon.

Lecture Notes

Aims of the course

The course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems and related eigenvalue problems and parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises involve Matlab implementation of Finite Element methods.

Participants of the course should become familiar with:

• concepts underlying the discretization of elliptic and parabolic boundary value problems
• analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems
• methods for the efficient solution of discrete boundary value problems
• implementiational aspects of the Finite Element method

Content of the course

• Elliptic boundary value problems
• Galerkin discretization of variational problems
• The primal Finite Element method
• Finite Difference and Finite Volume methods
• Mixed Finite Element methods

Optional topics

• Discretization of parabolic initial boundary value problems
• Discontinuous Galerkin methods
• Sparse grids

Matlab links

ETH students can download Matlab with a free network license from Stud-IDES (MATLAB free R2010x Stud).

• Matlab Online Documentation von MathWorks
• Matlab Primer
• Matlab Summary and Tutorial
• Matlab Online Documentation from the MathWorks
• Matlab Guide, D.J. Higham and N.J. Higham, SIAM 2000, ISBN 0-89871-516-4
• Matlab Einführungskurs, P. Arbenz

Literature

recommended literature:

• D. Braess, Finite Elements, 3rd Edition, Cambridge University Press, 2007 (or German original)
• S. Brenner and R. Scott, The Mathematical Theory of Finite Element Methods, 2nd Edition, Springer, 2002

additional literature:

• P. Knabner and L. Angermann, Numerical Methods for Elliptic and Parabolic Partial Differential Equations, Springer, 2003
• Ch. Grossmann and H.-G. Roos, Numerik partieller Differentialgleichungen, 2nd Edition, Teubner, 1994
• S. Sauter and Ch. Schwab, Randelementmethoden, Teubner, 2004
• V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, 2nd Edition, Springer Verlag, 2006